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Problem 45 Hard Difficulty

Given the following vector fields and oriented curves $C,$evaluate $\int_{C} \mathbf{F} \cdot \mathbf{T} d s$.
$\mathbf{F}=\frac{\langle x, y\rangle}{\left(x^{2}+y^{2}\right)^{3 / 2}}$ on the curve $\mathbf{r}(t)=\left\langle t^{2}, 3 t^{2}\right\rangle,$ for $1 \leq t \leq 2$

Answer

$\frac{3}{4 \sqrt{10}}$

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Video Transcript

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